Problem: Rewrite as a simplified fraction. ${2.2\overline{67} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}1000x &= 2267.6767...\\ 10x &= 22.6767...\end{aligned}}$ Subtracting the two equations, we have: ${990x = 2245}$ ${x = \dfrac{2245}{990}} $ ${x = \dfrac{449}{198}} \text{or} {2 \dfrac{53}{198}}$